We present the results from three gravitational-wave searches for coalescing
compact binaries with component masses above 1$\mathrm{M}_\odot$ during the
first and second observing runs of the Advanced gravitational-wave detector
network. During the first observing run (O1), from September $12^\mathrm{th}$,
2015 to January $19^\mathrm{th}$, 2016, gravitational waves from three binary
black hole mergers were detected. The second observing run (O2), which ran from
November $30^\mathrm{th}$, 2016 to August $25^\mathrm{th}$, 2017, saw the first
detection of gravitational waves from a binary neutron star inspiral, in
addition to the observation of gravitational waves from a total of seven binary
black hole mergers, four of which we report here for the first time: GW170729,
GW170809, GW170818 and GW170823. For all significant gravitational-wave events,
we provide estimates of the source properties. The detected binary black holes
have total masses between $18.6_{-0.7}^{+3.1}\mathrm{M}_\odot$, and
$85.1_{-10.9}^{+15.6} \mathrm{M}_\odot$, and range in distance between
$320_{-110}^{+120}$ Mpc and $2750_{-1320}^{+1350}$ Mpc. No neutron star - black
hole mergers were detected. In addition to highly significant
gravitational-wave events, we also provide a list of marginal event candidates
with an estimated false alarm rate less than 1 per 30 days. From these results
over the first two observing runs, which include approximately one
gravitational-wave detection per 15 days of data searched, we infer merger
rates at the 90% confidence intervals of 110 - 3840
$\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$ for binary neutron stars and 9.7 - 101
$\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$ for binary black holes, and determine a
neutron star - black hole merger rate 90% upper limit of 610
$\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$.